{"paper":{"title":"Super-resolution by means of Beurling minimal extrapolation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"John J. Benedetto, Weilin Li","submitted_at":"2016-01-21T19:35:42Z","abstract_excerpt":"Let $M(\\mathbb{T}^d)$ be the space of complex bounded Radon measures defined on the $d$-dimensional torus group $(\\mathbb{R}/\\mathbb{Z})^d=\\mathbb{T}^d$, equipped with the total variation norm $\\|\\cdot\\|$; and let $\\hat\\mu$ denote the Fourier transform of $\\mu\\in M(\\mathbb{T}^d)$. We address the super-resolution problem: For given spectral (Fourier transform) data defined on a finite set $\\Lambda\\subset\\mathbb{Z}^d$, determine if there is a unique $\\mu\\in M(\\mathbb{T}^d)$ of minimal norm for which $\\hat\\mu$ equals this data on $\\Lambda$. Without additional assumptions on $\\mu$ and $\\Lambda$, o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.05761","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}